Instability of the Chiral-Invariant Vacuum for a Confining Potential

Amer, A.; Yaouanc, A. Le; Oliver, L.; Pène, O.; Raynal, J.

doi:10.1103/physrevlett.50.87

Cited by 86 publications

(141 citation statements)

References 5 publications

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“…We find that for a whole range of allowed powers, 0 α 2, replica solutions do exist, similarly to the case of α = 2 studied in detail in [3,4]. We give the profiles of several replicas for the linear confinement and argue that the number of such solutions is infinite for any power α, including the weakest, logarithmic, potential which corresponds to α = 0.…”

Section: Introductionmentioning

confidence: 81%

“…The standard technique used in such models is the Bogoliubov-Valatin transformation from bare to dressed quarks parametrised by the chiral angle -the main entity defining the chiral symmetry breaking, the structure of the BCS vacuum of the theory, as well as the properties of the hadronic states built over this vacuum [3,4]. For the application of this technique to the two-dimensional QCD [9] see the papers [10].…”

Section: The Mass-gap Equationmentioning

confidence: 99%

“…The problem of instability of the chirally invariant vacuum for power-like confining potentials was studied in detail in the middle of 80's by the Orsay group [3] and such an instability was proved for the range 0 α < 3. For numerical studies the harmonic oscillator type potential, α = 2, was chosen by these authors, as well as by the Lisbon group [4], and a set of results for hadronic properties were obtained in the framework of the given model.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chiral symmetry breaking solutions for QCD in the truncated Coulomb gauge

Bicudo¹,

Nefediev

2003

Phys. Rev. D

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In this paper we study the power-like confining potentials r α . The region of allowed α's is identified, the mass-gap equation is constructed for an arbitrary α and solved for several values of the latter, and the vacuum energy and the chiral condensate are calculated. The question of replica solutions to the mass-gap equation for such potentials is addressed and it is demonstrated that the number of replicas is infinite for any α, as a consequence of the peculiar behaviour of the quark self-energy in the infrared domain.

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Section: Introductionmentioning

confidence: 81%

Section: The Mass-gap Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chiral symmetry breaking solutions for QCD in the truncated Coulomb gauge

Bicudo¹,

Nefediev

2003

Phys. Rev. D

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“…By this effective interaction Hamiltonian, mass and decay of heavy quarkonium states, 6 the quark condensation 11 and the chiral symmetry breaking 12 have been studied. The off-diagonal f (r) is the transition potential connecting the cc channels and the MM channels.…”

Section: Brief Survey Of the Frameworkmentioning

confidence: 99%

A Partial Width Calculation of OZI-Allowed Charmonium Decays in a Coupled Channel Framework

et al. 2009

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Abstract. OZI-allowed partial decay widths, masses, and total decay width of charmonium states are studied in a nonrelativistic coupled-channel framework based on microscopic effective quark interactions. With the help of the complex scale transformation, the coupled channel equation is easily solved under the proper boundary condition for resonances. The obtained result as a whole is very successful and encouraging for the traditional charmonium states including ψ(4040) whose features of mass and partial decay widths have been argued historically. The coupling mechanisms of these states are investigated by reducing artificially the channel coupling strengths little by little and finally turning the coupling off. The situations turn out to be quite different from what we would have naively supposed. Other solutions than the traditional charmonium states were obatined at the same time. Some of them are discussed in relation with new particles observed recently.

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“…This type of kernels has been extensively used in hadronic phenomenology [12,13]. In this case, we write the total Hamiltonian in normalordered form with respect to the new vacuum.…”

Section: The Approachmentioning

confidence: 99%

The effect of nonlocal confining kernels on magnetic chiral condensates

Felipe¹,

Marques

Ribeiro

2006

Nuclear Physics A

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The physics of spontaneous chiral symmetry breaking in the case of the simultaneous presence of a magnetic field and a fermionic quartic interaction is discussed for both local and nonlocal kernels in 2+1 and 3+1 dimensions. The approach is based on the use of Valatin-Bogoliubov canonical transformations, which allow, in the absence of fermionic quartic terms, to completely diagonalize the Hamiltonian and construct the vacuum state.

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Instability of the Chiral-Invariant Vacuum for a Confining Potential

Cited by 86 publications

References 5 publications

Chiral symmetry breaking solutions for QCD in the truncated Coulomb gauge

Chiral symmetry breaking solutions for QCD in the truncated Coulomb gauge

A Partial Width Calculation of OZI-Allowed Charmonium Decays in a Coupled Channel Framework

The effect of nonlocal confining kernels on magnetic chiral condensates

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